Pennsylvania has consistently received low ranks on measures of school
funding equity. As of 2008, prior to the implementation of a new funding formula,
Pennsylvania ranked 8th among all states in terms of school finance inequity, based on
the average percentage difference in per-pupil spending among school districts (Federal
Education Budget Project). While other states have altered their school funding
formulas as the result of court-ordered mandates, Pennsylvania’s legislature confronted
the issue directly, commissioning a costing-out study to establish the actual resources
necessary to ensure that the students of Pennsylvania receive an adequate education.55
In response to the recommendations of this study, the governor proposed a budget that
included additional funds to be directed to certain districts. The budget, along with a
new school funding formula, was enacted by the legislature in the summer of 2008.
Pennsylvania’s new formula sets an adequacy target determined by the number of students in each school district and their educational needs. Specifically, a base cost
of $8,003 is allotted for each student, and then additional funding is provided based on
the number of low-income students and English language-learners, the district’s size,
and regional cost differences (Augenblick, Palaich & Associates, 2007). Districts that
are unable to raise sufficient funds to meet the adequacy target are provided with state
funds to cover the gap. Of the 501 districts in the state of Pennsylvania, 471 districts
55 This work was instigated by a group of business leaders in the Lehigh Valley (Education 2010) who had commissioned Augenblick, Palaich & Associates to study the Allentown School District. The consultant’s analysis revealed a $2000 per pupil revenue gap which, in part, was the result of the state’s funding formula to districts (“Pennsylvania’s Costing-Out Study,” n.d.).
had spending below the estimate of what it would take to have their children reach an
adequate level.
For the purposes of the costing-out study, an adequate education is defined as
100% of students achieving proficiency on state reading and mathematics assessments
and mastering state standards in 12 academic areas by the year 2014 (Augenblick,
Palaich & Associates, 2007). Per pupil allotments include the cost of educating an
average student in the Commonwealth to meet state performance expectations plus
“weights” for certain categories of students (including students in poverty, special education students, gifted students, and English language learners) to allow them to
also meet state performance expectations.
The authors of the costing-out study used three methods to determine the
appropriate per pupil allotments: a successful school district approach, which examines
the spending of high performing school districts as measured against state performance
expectations; a professional judgment approach, which relies on the expertise and
experience of educators to specify the resources, staff, and programs that schools need
to meet performance expectations; and an evidence based approach, which uses
education research to help provide answers about how resources should be deployed in
schools so that students can meet performance expectations (Augenblick, Palaich and
Associates, 2007). Findings of these analyses led Augenblick, Palaich and Associates to
develop a new state funding formula designed to enable all districts to reach their
proficiency goals. Table 1 describes the weights tied to student needs used to determine
Table 1. Value of Formula for Factor Related to Student-Based Need
Student-Based Need Value or Formula for Factor
Special Education 1.30 x all students enrolled in special education programs
Poverty 0.43 x number of students eligible for
free/ reduced-price lunch English-Language
Learners
((-.023) x (LN of 2005-06 enrollment) +3.753) x number of ELL students, with a minimum of 1.48 and a maximum of 2.43 [ASD: 1.4978 x number of ELL students]
Gifted ((-0.13) x (LN of 2005-06 enrollment) +
1.482) x number of gifted students, with a minimum of .20 and a maximum of .66
[ASD: 0.2052 x number of gifted students]
Note. Adapted from Costing-Out the Resources Needed to Meet Pennsylvania’s Public Education Goals
(p. 30), by Augenblick, Palaich and Associates, Inc., 2007.
The school funding formula adopted by the state is designed to ensure that
education funds are distributed among districts to ensure vertical equity. Such an
approach is intended to provide for an adequate education for all students. This formula
provides a basis for defining equity in Pennsylvania.
Governance and Resource Allocation in Allentown School District
The Allentown School District operates with a $233 million budget and
employs more than 2,300 educators and support staff (school year 2010-2011), making
it the sixth largest employer in the Lehigh Valley. The Allentown School Board sets
policies for the district, guided by the Pennsylvania School Code. It is also engaged in
long-range planning and formal and informal evaluation of district initiatives. Required
duties of the Board include levying taxes, electing the superintendent and all district
employees, approving matters relating to investments and expenditures, and adopting
the annual budget. Nine school directors are elected by district residents to serve on the
state officials designated by law to administer the school system. The superintendent
and the administrative team support the board in all educational and financial actions
(ASD Board Brochure), and the superintendent serves as a non-voting member of the
board.
Budgets for the Allentown School District are prepared by the Chief Financial
Officer in cooperation with district administrators. All budgets are informed by
contracts with the various public employee unions operating in the district as well as
state and federal requirements. Procedures for allocating funds among schools and
programs have evolved over the years but appear to be comparable to the vast majority
of school districts in the United States. Budgeting is centralized and comprehensive
school-level budgets are not produced. To satisfy ESEA requirements for Title I
allotments, the district provides teacher average costs at the school level rather than
including actual costs. Specific methods for resource allocation are reported in greater
detail in Chapter V. In school year 2010-2011, the administration in Allentown hired
the education consulting firm of Cross & Joftus56 to conduct a resource assessment,
providing district personal with detailed information of how and where money was
being spent in the 2009-2010 school year.
Data Collection
All data collection has been approved by the Allentown School District and the
University of Pennsylvania Institutional Review Board. Data collection took place
during the 2010-2011 school year and consists of document analysis and interviews; the
analysis is based on 2009-2010 data.
The information used to complete this study includes data on students, teachers,
and schools. Student data includes student characteristics (i.e., ELL status, poverty,
race, special education status), student achievement data (i.e., Pennsylvania System of
School Assessment scores, AYP performance levels), and student behavior data (i.e.,
attendance, disciplinary actions). This data is collected at the district and state level and
reported by the state.
Teacher data includes teacher attributes57 (i.e., years of experience, credentials),
teacher compensation, and metrics of professional practice (i.e., evaluation reports,
value-added scores, teacher self-efficacy measures, teacher collective-efficacy
measures). Information on teachers’ attributes presents the greatest difficulty in terms
of data collection. The human resources department has data on teachers’ years of
experience, credentials (e.g., B.S., M.S.), professional development courses taken,
teachers’ certification status, and teachers’ college attended and grade point average in personnel files in the Administration Building. The department does not keep PRAXIS
test scores, which could serve as a proxy for content and pedagogical knowledge.
Unfortunately, teacher data has not yet been transferred to a centralized personnel
database, so only information on experience and credentials is available for my study.
Data collected on teacher compensation include salary, benefits, and funding source.
57 I was unable to attain reliable teacher data on general academic ability, training, or certification status – beyond the fact that all teachers in elementary schools and middles schools are “highly qualified” as required by No Child Left Behind federal legislation.
Amassing metrics of professional practice required some additional collection
of data. The district’s only available measure of individual teacher practice is an evaluation report that indicates whether teachers are “satisfactory” or “unsatisfactory.” Over 98% of teachers were categorized as “satisfactory” in the 2009-2010 school year.
As this finding does not provide much discrimination for an equity analysis, I have not
used it in my study. Two district initiatives were implemented in the 2011 to support
the collection of measures of teacher practice: first, the district contracted with SAS
EVAAS to provide teacher level value added scores; and second, I administered a
survey to all the teachers in the district to question their sense of self-efficacy and the
collective efficacy of the building in which they work.
As a result of additional data collection, I have four measures of human capital
resources that have not been included in the literature on intradistrict equity. The first
metric of professional practice which I use in my analysis is ratings of teachers
according to their value-added scores. This metric is used to differentiate among
schools on the basis of the portion of highly effective teachers in each school and the
portion of highly ineffective teachers in each school. The second metric used in my
analysis is a calculation of teacher efficacy determined using data from a survey
administered to all elementary and middle school teachers. Two additional measures
are similar in that they rely of value-added measures and efficacy measures, but they
differ in that they offer a view of what the entire school offers to students. The Growth
tested grade levels in schools. Teacher collective efficacy measure provides teachers
perspectives regarding their schools’ faculty, as a whole, to impact student outcomes. Value added measurements of low and high teacher effect. Teachers have long
been acknowledged for their students' accomplishments. Many have pointed out that
this is unfair, as teachers are only responsible for a portion of student achievement
outcomes. Value-added models were developed to address this problem. In theory, they
partition out student growth that is the result of the classroom environment, or teacher
practice, and the growth that is due to what the student brings to the classroom: her
prior knowledge, the support of her family, previous teachers, etc. After these factors
have been separated these models can, essentially, rate teachers based on their
contribution to student achievement outcomes.
Value-added models rely on student assessment results and links between
teachers and students. Data systems have been enhanced in recent years, making the
application of value-added models possible though approach only offers information on
teachers that are teaching tested grades and subjects (such as Mathematics and English
Language Arts). To date, the information generated through the PA Value-added
assessment system has been primarily used as a tool to aid teachers in their instruction.
For example, value-added results can identify the type of students (high achieving or
low achieving) with which the individual teachers are achieving the best results. This
information can be used to target appropriate supports to teachers.
The more data that is included in value-added models, the more accurate their
As previously discussed, there are additional technical concerns that must be
acknowledged when using value-added models to measure teacher effectiveness: one
such concern is that value-added models generally assume that students are randomly
assigned to classrooms, which is often not the case. Also, a teachers' influence may go
beyond his classroom, thereby skewing the results for other teachers. Additionally, not
all value-added models are the same - and some provide better information than others.
More practical concerns include the fact that value-added models are complex and
difficult to explain.
While the state does not provide teacher level value added scores to school
districts, it is possible to obtain this information if the district is willing to provide
teacher level data and student level data, and links between them, to an organization
with the capacity to conduct the analysis. ASD has contracted with SAS EVAAS to
provide teacher-level value-added scores for all elementary school teachers in grades
four through five and middle school teachers teaching mathematics and English
Language Arts in grades six through eight. Students in these grades must take the
Pennsylvania System of School Assessment (PSSA), providing the data required to
conduct value-added analysis.58 Using a longitudinal, mixed model approach, SAS
EVAAS offers a complex statistical model which provides less vulnerable outcomes
than simple value-added models (McCaffrey, Han & Lockwood, 2008). Furthermore,
SAS EVAAS methodology has been approved as a viable growth model for states and
58 SAS EVAAS currently has a contract with the State to provide school- and district-level value added data.
districts to include in their Teacher Incentive Fund and Race to the Top applications59
(U.S. Department of Education website).
With data on student PSSA scores, and links to teachers provided by the district,
SAS EVAAS was able to construct a teacher level value-added measure. This measure
compares teachers within the district and divides these teachers into quintiles according
to their effectiveness. Definitions for these quintiles are provided below:
Level 1, Least Effective: Teachers whose students are making substantially less progress than state growth standard (the teacher’s index is less than -2).
Level 2, Approaching Average Effectiveness: Teachers whose students are making less progress than the state growth standard (the teacher’s index is less than -1 but equal or greater than -2).
Level 3, Average Effectiveness: Teachers whose students are making the same amount of progress as the state growth standard (the teacher's index is less than
1 but equal to or greater than -1).
Level 4, Above Average Effectiveness: Teachers whose students are making more progress than the state growth standard (the teacher's index is less than 2
but equal to or greater than 1);
Level 5, Most Effective: Teachers whose students are making substantially more progress than the state growth standard (the teacher's index is 2 or
greater).
59 The first two growth model pilots awarded by the U.S. Department of Education were awarded to Tennessee and North Carolina, each engaging SAS EVAAS to provide value-added analysis.
For my equity analysis, I look at how teachers are dispersed among schools
according to their effectiveness as defined above. More specifically, I consider schools
in two ways: 1) by percentage of teachers60 in bottom two quintiles of effectiveness
(least effective and approaching average effectiveness); and 2) by percentage of
teachers61 in top two quintiles of effectiveness (above average effectiveness and most
effective).
Three-hundred-forty-one (341) value-added measures were provided for elementary
and middle schools. There are 819 teachers in elementary and middle school. This
represents only 31% of all teachers. This is due to a number of reasons: 1) in
elementary schools, the majority of scored teachers get rankings for both reading and
mathematics; 2) in elementary schools, only teachers in grades four and five are
included in the calculus; and 3) value-added scores were only provided for teachers
with two years of data available. Table 2 provides school level data.
60 This is calculated only for teachers with value-added scores. 61 This is calculated only for teachers with value-added scores.
Table 2. Number and Percentage of Teacher-Level Value Added Scores by School School Number of Teachers included in Analysis Total Number of Teachers in the Building % of all Teachers included in Analysis McKinley ES 4 18.4 22% Lehigh Parkway ES 1 18.1 6% Cleveland ES 5 18.5 27% Jackson ES 5 18.4 27% Ritter ES 8 32.4 25% Washington ES 9 39.2 23% Muhlenberg ES 7 34.8 20% Sheridan ES 7 42.2 17% Jefferson ES 7 50.1 14% Roosevelt ES 4 36.5 11% Mosser ES 4 46.2 9% Hiram Dodd ES 7 46.2 15% Union Terrace ES 9 43.2 21% Central ES 10 50.3 20% Harrison-Morton MS 42 56.0 75% Raub MS 42 67.1 63% Trexler MS 47 68.3 69% South Mountain MS 36 84.6 43%
Given the small sample size of teachers with value-added scores, especially in
elementary schools, this data should be considered with great caution. Also, while this
metric may be more useful in middle schools where a greater number of teachers are
included in the analysis, there is still an issue stemming from the variation among
schools in the percent of all teachers included in the analysis. As demonstrated in the table above, Harrison-Morton Middle School has scores for 75% of its teachers while
South Mountain Middle School has scores for only 43% of its teachers.
Growth Index. Just as teacher effectiveness is determined through an analysis
of what “value” teachers add, the Growth Index similarly provides a measure of what “value” an entire school adds. According to an informational document provided by
one of the state’s Intermediate Units (IU5), “the index is a value based on the average growth across grade levels and its relationship to the standard error so that comparison
among schools is meaningful” (IU5, 2011, p.4) A growth index of fifty indicates that, on average, students in the school achieved a year’s worth of academic growth in a year.62 A growth index greater than fifty indicates that, on average, students in the
school achieved more than a year’s worth of academic growth in a year and a growth
index less than fifty indicates that, on average, students in the school achieved less than
a year’s worth of academic growth in a year (IU5, 2011). In my equity analysis, I consider how the State’s calculated growth index for each school varies by school. Teacher efficacy. An additional input that has not been included in research on
intradistrict equity is that of teacher efficacy. As noted earlier, both teacher self-
efficacy and teacher collective efficacy have shown to be related to student outcomes.
As such, it is worthwhile to include these metrics as measures of teacher quality,
resources which are potentially differentially distributed across schools. In order to
evaluate teacher efficacy, I administered a survey to all teachers in ASD. (The email
sent to principals requesting that they have the teachers in their building respond to an
email survey is included in Appendix D.) The survey presented to teachers included 25
responses: the first response required was to indicate in which building the respondents’
primary teaching responsibilities lay. The following twelve items measured teacher
self-efficacy, and the final twelve questions measured teacher collective efficacy.
Survey response was high. Assuming that all teachers, and only teachers, received the
62 The Growth Index provided by the State uses zero to indicate a year’s worth of growth in a year. I have transformed their numbers in order to accurately apply my equity statistics.
request to complete the survey, 79% (429) elementary school teachers responded and
91% (251) middle school teachers responded.63
My dissertation uses the Teacher Beliefs Scale – short form (TBS), originally